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Math Help - Questions about Logs and similar type word problems

  1. #1
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    Questions about Logs and similar type word problems

    Hey guys I have a couple of questions about the topic stated above that I simply do not understand.
    If you could help, it would be greatly appreciated.

    These were questions in the textbook that I did not understand and with no answer in the back of the book. I have a test tomorrow and I am truly confused. If you could do out some of the problems and explain the steps, it would be greatly appreciated.

    1. 8-2e^-x = 4

    2. 7^x+3 = e^x

    3. log(subscript 2)(x-4) + log(subscript 2)(x+4)=3

    4. write [log(subscript 2) ((4x^3)/(x^2-3x-18))] as the sum and/or difference of logarithms

    5. e^(x^2)=(e^3x)(1/e^2)

    6. Using the graph of the exponential function y=3^x -1:

    a. What is the value when x=4
    b. what is the value when x=0
    c. what is the domain
    d. what is the range?
    e. What is the horizontal asymptote?

    7. A colony of bacteria grows according to the following function: N(t)= 200e^.045t where N is measured in grams and t is measured in days
    a. what is the initial amount of the bacteria?
    b. what is the growth factor?
    c. what is the population of the bacteria after 5 days?
    d. How long will it take the population to double?

    8. Traces of burned wood along with ancient tools were found to contain approximately 2.67% of the original amount of carbon. If the half-life of carbon is 550 years, approximately when was the tree cut and burned?
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  2. #2
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    Quote Originally Posted by falconskid007 View Post
    Hey guys I have a couple of questions <<<<<<< taking the number of questions into account that must be polygamy
    about the topic stated above that I simply do not understand.
    If you could help, it would be greatly appreciated.

    These were questions in the textbook that I did not understand and with no answer in the back of the book. I have a test tomorrow and I am truly confused. If you could do out some of the problems and explain the steps, it would be greatly appreciated.

    1. 8-2e^-x = 4

    ...
    1. Please don't publish so many questions in one post. (Read the forum's rules!)

    to #1. You have to transform the equation until only the power of e is left at one side of the equation:

    8-2e^{-x} = 4~\implies~-2e^{-x}=-4~\implies~e^{-x}=2~\implies~e^x=\frac12

    Now calculate x by taking the logarithms at both sides of the equation.
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